Solve x^2=2x+48 and x^2=30-7x by factoring

Answer 1

x² = 2x + 48 ==> 0 = x² - 2x -48

Now find the factors of 48: 48/1;24/2;16/3;12/4;8/6

Out of those only 8 & 6 can be used to make -2,

when you subtract 8 from 6.

Therefore the factors are 6 & -8

( x + 6 )( x - 8 )

---

x² = 30 - 7x ==> 0 = x² + 7x -30

Find factors of 30: 30/1;15/2;10/3;6/5

Only 10 & 3 can be used to make 7

when you subtract 3 from 10.

Therefore the factors are 10 & -3.

( x + 10 )( x - 3 )